Problem 7.A company is interviewing potential employees. Suppose that each candi

Question

Problem 7.A company is interviewing potential employees. Suppose that each candidate is either qualified, or unqualified with given probabilities q and 1- q, re- spectively. The company tries to determine a candidate's qualifications by asking 20 true-false questions. A qualified candidate has probability p of answering a question correctly, while an unqualified candidate has a probability p of answering incorrectly. The answers to different questions are assumed to be independent. If the company con- siders anyone with at least 15 correct answers qualified, and everyone else unqualified, give a formula for the probability that the 20 questions will correctly identify someone to be qualified or unqualified.

Explanation / Answer

Here, we can use the binomial distribution and formula to be used would be as under: -

n!/x!(n-x)!*p^x*q^n-x

Where n would be the number of questions i.e. 20, x would be the number of questions to be answered correctly i.e. 15, 16, 17, 18, 19 and 20. p would be the probability of answering the question correctly/incorrectly and q would be 1-p.

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